Multi-antenna techniques are used in communication systems to improve performance. These techniques rely on multiple antennas at the transmitter and/or receiver and can be grouped into three different categories: diversity, beamforming, and spatial multiplexing. These three categories are often collectively referred to as MIMO communication.
To provide a specific example of MIMO communication, consider the wireless communication system 100 shown in FIG. 1 that includes a transmitter 102 with two transmit antennas 104-1 and 104-2 and a receiver 106 with two receive antennas 108-1 and 108-2. Spatial separation between the two antennas at both the transmitter 102 and the receiver 106 create different sub-channels, each including different signal paths and signal path lengths, across the wireless channel 110. For example, the signal path length of the sub-channel between the transmit antenna 104-1 to the receive antenna 108-1 is different from the signal path length of the sub-channel between the same transmit antenna 104-1 to the receive antenna 108-2. Because of these differences in signal path lengths (and for other differences in the sub-channels), a signal transmitted from either one of the transmit antennas 104-1 and 104-2 will arrive at the receive antennas 108-1 and 108-2 with different phase shifts. These different phase shifts can be respectively represented by the channel elements h11, h12, h21, and h22 as shown in FIG. 1, or by the channel matrix H given by:
                    H        =                  (                                                                      h                  11                                                                              h                  21                                                                                                      h                  12                                                                              h                  22                                                              )                                    (        1        )            
Assuming knowledge about the channel matrix H can be determined and that the channel matrix H is invertible, it is possible to transmit different signals from the transmit antennas 104-1 and 104-2 in parallel and separate the different signals at the receiver 106 using the MIMO communication technique of spatial multiplexing. For example, as further shown in FIG. 1, the two transmit antennas 104-1 and 104-2 can respectively transmit, in parallel, two different signals s1 and s2. The resulting signals r1 and r2 respectively received by the receive antennas 108-1 and 108-2 can be expressed as:
                                          r            _                    =                                    (                                                                                          r                      1                                                                                                                                  r                      2                                                                                  )                        =                          (                                                                                          h                      11                                                                                                  h                      21                                                                                                                                  h                      12                                                                                                  h                      22                                                                                  )                                      ,                                            (                                                                                          s                      1                                                                                                                                  s                      2                                                                                  )                        +                          (                                                                                          n                      1                                                                                                                                  n                      2                                                                                  )                                =                                    H              ·                              s                _                                      +                          n              _                                                          (        2        )            where n is a vector consisting of noise elements n1 and n2 that impair the signals received at the different receive antennas 108-1 and 108-2. The transmitted signals s1 and s2 can be recovered at the receiver 106 with no interference between the signals by multiplying the received vector r by the inverse of the channel matrix H.
The above represents one method for performing spatial multiplexing. Other methods include, for example, using a linear precoder at the transmitter to effectively “orthogonalize” the parallel transmissions from the transmitter 102. Specifically, the channel matrix H (or some estimate of the channel matrix H) can first be expressed as its singular-value decomposition (SVD):H=U·Σ·V*  (3)where U is an NRX by NTX unitary matrix, Σ is an NTX by NTX diagonal matrix, V is an NTX by NTX unitary matrix, and NRX and NTX respectively represent the number of antennas at the receiver and transmitter. After expressing the channel matrix H as its SVD, the matrix V can be applied at the transmitter by the linear precoder and U* can be applied at the receiver, leaving an equivalent channel matrix equal to the matrix a Because the matrix Σ is diagonal, the spatially multiplexed signals are effectively “orthogonalized” and do not interfere at the receiver.
In general, accurate knowledge of the channel matrix H is essential to reducing residual interference between signals s1 and s2 transmitted in parallel over the channel using any method of spatial multiplexing. However, even with perfect knowledge of the channel matrix H, inherent sources of phase noise present in the transmitter 102 and the receiver 106 will result in residual interference between the signals s1 and s2 at the receiver. In particular, local oscillator signals used to up-convert the signals s1 and s2 at the transmitter 102 for transmission and down-convert the signals r1 and r2 for demodulation at the receiver 106 include phase noise. The spectrum of an ideal local oscillator signal assumes the shape of an impulse. In practice, however, phase noise is seen in the spectrum of a local oscillator signal as random fluctuations or “skirting” around the impulse. If not accounted for, this phase noise can corrupt the resulting up-converted or down-converted signals and result in residual interference between the signals s1 and s2 at the receiver 106.
One conventional approach to dealing with local oscillator phase noise in MIMO communication systems has been the use of a shared local oscillator signal at the transmitter and/or at the receiver. However, in many wireless communication systems, such an approach is not practical. For example, in wireless backhaul systems using MIMO communication, often a local oscillator signal cannot be shared by all transmitters and/or receivers because the antennas need to be placed relatively far apart (e.g., up to several meters apart) to ensure low signal path correlation. With relatively large distances separating the antennas, high frequency local oscillator signals, such as those used in microwave and millimeter-wave backhaul links, cannot be practicably shared.
The embodiments of the present disclosure will be described with reference to the accompanying drawings. The drawing in which an element first appears is typically indicated by the leftmost digit(s) in the corresponding reference number.